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Keymaster
Post count: 802

Solve $$\frac{x-10}{2}=6$$.

$$\frac{x-10}{\cancel{2}}^{\cancel{\times2}}=6^{\times2}$$     multiply both sides by 2

x – 10 = 12   add 10 to both sides

x = 22

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Keymaster
Post count: 802

The sum of three consecutive even numbers is 84. If the middle number is 2x + 4, what is the value of x?

consecutive means in a row so the one before it would be: (2x + 4) – 1 = 2x + 3
the one after it would be (2x + 4) + 1 = 2x + 5
first number: 2x + 3 middle number: 2x + 4 last number: 2x + 5
2x + 3 + 2x + 4 + 2x + 5 = 84
6x + 12 = 84
6x = 72
x = 12

Keymaster
Post count: 802

If X = 2a + b and Y = a – b, then find the value of a + 2b.

(X = 2a + b)  – (Y = a – b)

X – Y = 2a – a + b – -b

X – Y = a + 2b

∴ a + 2b = X – Y

 Solve 12500 = 36500(1 – r)³ for r. $$\frac{12500}{36500}=(1-r)^3$$ $$\frac{25}{73}=(1-r)^3$$ divide both sides by 36,500 $$\sqrt[3]{\frac{25}{73}}=1-r$$ take the cube root of both sides, cancelling the cube on the right $$\sqrt[3]{\frac{25}{73}}+r=1$$ add r to both sides $$r=1-\sqrt[3]{\frac{25}{73}}$$ subtract $$\sqrt[3]{\frac{25}{73}}$$ from both sides r = 0.3 calculate